Enhancing optoelectronic properties of SiC-grown graphene by a surface layer of colloidal quantum dots

We report a simultaneous increase of carrier concentration, mobility and photoresponsivity when SiC-grown graphene is decorated with a surface layer of colloidal PbS quantum dots, which act as electron donors. The charge on the ionised dots is spatially correlated with defect charges on the SiC-graphene interface, thus enhancing both electron carrier density and mobility. This charge-correlation model is supported by Monte Carlo simulations of electron transport and used to explain the unexpected 3-fold increase of mobility with increasing electron density. The enhanced carrier concentration and mobility give rise to Shubnikov-de Haas oscillations in the magnetoresistance, which provide an estimate of the electron cyclotron mass in graphene at high densities and Fermi energies up to 1.2  ×  1013 cm−2 and 400 meV, respectively.

controlling the electronic properties of graphene, including its photosensitivity, is to functionalise it chemically or combine it with nanomaterials.
Here we demonstrate that the electrical and optical properties of n-type graphene on SiC can be significantly enhanced by decorating the graphene surface with a layer of colloidal PbS quantum dots (QDs), which act as electron donors. This leads to a significant increase of the electron concentration in graphene from = × n 5.2 10 12 cm −2 to = × n 1.2 10 13 cm −2 , accompanied by a remarkable 3-fold enhancement of the low-temperature mobility, which we attribute to a reduction of elastic scattering due to a charge correlation effect. This enhancement of the electrical properties enables the observation of Shubnikov-de Haas (SdH) magnetoresistance oscillations and allows us to estimate the electron cyclotron mass in graphene up to Fermi energies of 400 meV above the Dirac point, significantly higher than those reported previously [12]. The presence of the PbS QDs, which are optically active in the near infrared spectral range, also produces a device with a strong photoresponsivity of up to = R 10 5 A W −1 . We explain our measurements in terms of the Enhancing optoelectronic properties of SiC-grown graphene by a surface layer of colloidal quantum dots 2 transfer of electronic charge from the QDs to the graphene layer and of the spatial correlation of the charges in these two layers. Our Monte Carlo simulations of the electron transport in graphene provide additional support to this model. These results are relevant to the future exploitation of SiC-grown SLG in functional devices.
The SiC-grown graphene (SiC-SLG) [13,14] was processed into Hall Bars with a channel width w = 20 µm and length L = 100 µm, as shown in figure 1(a). The electrical properties and photoresponse were measured firstly on control samples, i.e. pristine SiC graphene devices. The devices were then decorated with a layer of colloidal PbS QDs with an average PbS nanocrystal diameter of = d 4.5 PbS nm. PbS QDs were synthesised in aqueous solution and were capped with a mixture of thioglycerol and 2,3-dimercaptopropanol (TGL) of length ≈ l 0.5 nm ( figure 1(b)) [15]. To achieve full coverage of the SLG, the QD solution with concentration of 10 16 QDs ml −1 was drop-casted onto the graphene device and dried in vacuum at P ~ 10 −8 bar for 12 h. We note that once the QDs fully cover the graphene layer, any further increase in the thickness of the QD layer does not change significantly the properties of SLG. All electrical measurements were performed in a cryostat equipped with a superconducting magnet ( ⩽ B 14 T) in the temperature range 2 K < < T 250 K. We measured the photoresponse in vacuum at room temperature with excitation from a HeNe laser beam at λ = 633 nm and × P up to 5 10 3 W m −2 . The results of our Hall effect measurements of SLG with and without the QD layer are shown in the figure 1(c). The electrical properties of the pristine devices are typical of heavily doped SiC single-layer graphene. They have an almost temperature-independent electron concentration, = × n 5.2 10 12 cm −2 , and a Hall mobility which increases from µ = 720 cm 2 V −1 s −1 at = T 250 K to µ = 1000 cm 2 V −1 s −1 at T = 2 K. These graphene layers show no detectable photoresponse (figure 1(d)). Deposition of the QD layer leads to an increase of electron concentration to = × n 1.2 10 13 cm −2 , a value which remains roughly independent of temperature over a wide range from 2 K to 250 K, and to a significant increase in the Hall mobility, µ = 1600 cm 2 V −1 s −1 (T = 250 K) and 3000 cm 2 V −1 s −1 (T = 2 K). In addition, the deposition of the QD layer induces a very strong photoresponsivity of up to = R 10 5 A W −1 (inset in figure 1(d)), not achieved previously in SiC-graphene, and is comparable to that reported for QD-decorated CVD SLG [3]. The photocurrent is proportional to the applied bias.
The high value of photoresponsivity can be understood in terms of the long lifetime, τ QD , of photogenerated charge bound to the QDs, relative to the time, τ d , taken for an electron to drift down the length of the graphene channel [16]. The photoresponsivity is R / α τ ντ = e h QD d , where α is the optical absorbance of the PbS QDs [17] and From the measured value of R = 10 5 A W −1 , we esti-mate τ ≈ 0.1 QD s, comparable to the lifetime of holes reported in CVD graphene capped with similar QDs [16]. The photoresponsivity of QD-decorated graphene devices exhibits a power-law dependence of the type α − P , where α = 0.9 (inset in figure 1(d)), which was also observed previously [3,16,18]. The deviation from this power-law dependence at low incident powers is attributed to reduction of the signal-to-noise ratio.
The simultaneous increase of carrier concentration and mobility induced by the deposited QD layer is sufficient to observe a series of well-defined SdH oscillations in the low temperature magnetoresistance at magnetic fields, B 7 T, as shown in figures 1(c) and 2(a). Fourier analysis reveals that the oscillations, which are periodic in /B 1 , have a fundamental field, = B 129 f T. Assuming a Landau valley and spin degeneracy, = g 4, we obtain an electron sheet density SdH f 13 cm −2 , in close agreement with that obtained from the low field classical Hall effect.
The temperature dependence of the SdH oscillations (figure 2(a)) allows us to estimate the cyclotron effective mass of the electrons, m c , up to electron concentrations and Fermi energy significantly higher than reported previously [12]. We fit the dependence of the SdH amplitude on T and B to the following relation [12,19]: , where n is the electron sheet density. We obtain v F = 0.86 ± 0.06 × 10 6 m s −1 , which is in good agreement with that previously reported for exfoliated graphene [12] (green curve in the inset in figure 2(b)), but lower than that reported for SiC-grown graphene (v F = 1.02 ± 0.01 × 10 6 m s −1 ) [20,21]. Our result confirms that the energy-wavevector dispersion of SLG remains linear up to electron concentrations of 10 13 cm −2 and Fermi energies 400 meV. This suggests that the low values of mobility, typically observed in highly doped graphene, are not associated with the increase of SLG electron cyclotron mass at high Fermi energies.
We now consider the origin of the enhanced values for the carrier concentration and mobility in the QD-decorated graphene. The main mobility-limiting mechanism is usually associated with electron scattering on charged defects in the vicinity of the graphene layer and has been described by the phenomenological relation: where N is the concentration of the charged defects, N 0 = 10 10 cm −2 and α is a fitting parameter [22]. These charged defects can include the donor and/or acceptor species that determine the carrier concentration in graphene. Previous studies of the variation of SiC-SLG mobility with electron concentration [11] indicate that relation (2) is valid for SiC-SLG. However, our measured enhancement of both carrier concentration and mobility following the deposition of the QDs is clearly inconsistent with this relation. Furthermore, the model of electrostatic compensation and screening of impurities with opposite charges, previously used to explain the high mobility of CVD p-type SLG decorated with QDs [23] does not apply to our data on SiC-SLG/ QD devices since in this case the SLG is n-type.
To explain our findings, we propose a model based on spatial correlation of unipolar, positively charged defects in the QD and the adjacent SiC-SLG layers. We propose that the position of charge within each QD deposited onto graphene is influenced by the Coulomb repulsion by discrete charges near the surface of SiC-SLG; the charge on the QDs would then locate in regions with the lowest electrostatic potential energy. We model the charge distribution numerically by placing 10 -12 10 -11 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -6 10 -5  . Our measurements on the samples with different levels of QD coverage indicate that the deposition of additional layers beyond a mono-layer does not influence significantly the device performance. Thus we conclude that efficient charge transfer is predominantly from those QDs in direct contact with the graphene layer and that it is negligibly small between the QDs. Hence only the QD layer adjacent to the SLG makes a significant contribution to the charge correlation.
We find that a random deposition of QDs leads to the increased amplitude of the electrostatic potential fluctuations, calculated as a standard deviation, from δ = U 160 meV (pristine graphene, figure 3(a)) to δ = U 250 meV (graphene and randomly distributed QDs, figure 3(b)). In contrast, for the correlated distribution of QDs, the potential fluctuations are significantly smaller, with δ = U 30 meV (figure 3(c)). Our model therefore supports the conjecture that this reduction of the electrostatic potential fluctuations is responsible for the measured increase of carrier mobility.
We calculate the dependence of the carrier mobility, µ, on impurity density, N imp , for different degrees of spatial correlation of the charges by using an analytical model in which the correlation is quantified by the ratio of the maximum to minimum separations between the charged impurities [24]. The maximum distance corresponds to the case when the N imp charges are arranged in an ordered 2D array with the maximum impurity separation, r i , defined for hexagonal closed-packed (hcp) lattice as Any imperfection in this ordering leads to the reduction of interimpurity distance, r, in the range < < r r r i 0 , where r 0 is the minimum separation. The degree of correlation of the charged impurities is related to the ratio / r r i 0 , where / r r i 0 = 1 corresponds to an ordered distribution, and / = r r 0 i 0 to a random distribution. For low concentrations, N imp < 10 12 cm −2 , the mobility is almost independent of r 0 , indicating that the effect of charge correlation on mobility is negligible in high purity SLG. In this case there is no significant overlap of the electrostatic potentials of the charged impurities and the free carriers always move in a potential due to independ-ent single charges [8]. The model used in [22] considers only charged impurity scattering and does not include other mobility-limiting mechanisms, e.g. phonon scattering [23]. With increasing impurity concentration, the ratio of / r r i 0 increases and when / = r N 1.1 i imp approaches r 0 , the charged scattering-limited mobility becomes very large, reflecting the absence of scattering in an ordered potential ( figure 4(a)). For the pristine SiC graphene, our experimental values of carrier density and mobility ( figure 4(a)) correspond to no correlation (r 0 = 0), as in equation (2). The simultaneous increase of both carrier concentration and mobility following deposition of the QD layer cannot be explained by equation (2) (figure 4(a)). However, this result is successfully modelled using our correlated charge model with / = r r 0.7 i 0 and r 0 ≈ 2.1 nm, which is comparable with the nearest neighbour distance estimated for the correlated case in our numerical calcul ations (figure 3(c) and supplementary information, SI2) and with the radius of our QDs.
To complement our analytical model, we performed Monte Carlo simulations for our unipolar graphene-QD heterostructure. Our model is based on scattering by spatially correlated charges of the same x (nm) polarity, i.e. unipolar charges, and excludes charge compensation that would occur in the bipolar case [23]. First, we calculate the carrier mobility for the pristine SiC graphene assuming a random (uncorrelated) distribution of impurities in the SLG ( figure 3(a)). The values that we obtain for the mobility are in good agreement with equation (2) with α = 18 m 2 V −1 s −1 . The discrepancy between the experimental and numerical values of mobility is due to large uncertainties in the value of the phenomenological coefficient α (equation (2)). For the QD-decorated SLG we assume that QDs have a comparable effect on the electron mobility to that of the charged impurities in the SiC ( figure 4(b)). The calcul ation indicates that for > N N QD imp , the mobility is determined largely by the degree of spatial correlation of the defect and QD charges. For the case of no correlation ( figure 3(b)), we find a conventional decrease of mobility as described by equation (2). In contrast, as shown in figure 3(c), for the case of high correlation of charges, the Monte Carlo simulations indicate that significant increase of mobility is achieved, in good qualitative agreement with our analytical model and with the experimental results ( figure 4(a)).
In conclusion, we have measured a significant and simultaneous increase of the photoresponsivity, carrier concentration and mobility in SiC-grown graphene when it is decorated with a layer of colloidal PbS QDs. A unipolar charge correlation model was used to explain our observations. Our numerical calculations indicate that a flattening of the electrostatic potential fluctuations, resulting from the spatial charge correlation, reduces significantly scattering by charged impurities and hence leads to the measured increase of mobility. This conclusion is supported by Monte Carlo simulations of electron transport in our SLG devices. The high carrier concentration and mobility in our devices permits the observation of SdH oscillations and provides an estimate of the electron cyclotron mass in graphene at carrier concentrations up to 1.2 × 10 13 cm −2 . Our measurements suggest that the decoration of epitaxial graphene with a layer of colloidal QDs or other electrically and optically active capping layers could extend the potential of epitaxial graphene for technological applications.

Acknowledgments
The work is supported by The Leverhulme Trust (grant number RPG-2013-242), the Engineering and Physical Sciences Council (grant number EP/M012700/1), and the EU Graphene Flagship. Authors acknowledge useful discussions with Dr M W Fay and Prof N R Thomas.

Supporting information
Supporting information includes description of the calculations of the electrostatic potential landscape and analysis of 2D charge distribution

Table of content entry
Enhancing optoelectronic properties of SiC-grown graphene by a surface layer of colloidal quantum dots.
A simultaneous increase of carrier concentration, mobility and photoresponsivity is achieved in SiCgrown graphene decorated with colloidal PbS quant um dots, and explained by a unipolar charge-correlation model and Monte Carlo simulations of electron transport. The observation of Shubnikov-de Haas oscillations in these devices provide an estimate of the electron  cyclotron mass in graphene at high electron densities up to 1.2 × 10 13 cm −2 .